Under the AFL's measures announced at the start of the month, Cerra was referred directly to the tribunal after a collision with umpire Rob O'Gorman in last week's loss to Brisbane.
It was the fourth time he had been booked for the offence within two years, triggering the hearing instead of him being able to have an early guilty plea accepted.
The AFL is concerned about the growing prevalence of the collisions, which mostly happen at centre bounces.
Cerra, who watched the hearing via video link but didn't give any evidence, pleaded guilty.
The 25-year-old had been backing away from Lions opponent Lachie Neale late in the second quarter when he made contact with O'Gorman.
Carlton argued Cerra should only receive a $5000 fine, saying he likely would have contested previous charges had the direct referral for umpire contact been in place before this month.
However, the AFL pushed for the sanction to be $6250, meaning the two parties spent more an hour debating over $1250.
The tribunal spent 30 minutes deliberating before deciding to meet almost in the middle at $5550.
"To penalise Cerra for the higher number of umpire contacts this year would be unfair," Blues barrister Elizabeth Bateman told the panel.
"It would be punishing him for events that he has absolutely no control over."
In a busy night at the tribunal, Brisbane Lions premiership player Zac Bailey has failed to overturn a one-match ban for rough conduct.
The in-form Lion challenged his suspension for a high bump on Carlton defender Nick Haynes.
Brisbane's lawyer Adrian Anderson tried to have the charge downgraded from medium to low impact, meaning Bailey would be fined instead of missing this Friday night's clash with the Western Bulldogs.
Haynes was not injured in the incident and played out the match, but did touch his face to acknowledge there was high contact made.
Anderson used seven examples of bumps similar to Bailey's that were graded low.
But the tribunal disagreed and decided to accept the match review officer's grading of medium impact.
"The bump was high and had the potential to cause injury ... the tribunal is not bound by previous decisions," tribunal chair Jeff Gleeson said.
The last matter for the night is North Melbourne ruckman Tristan Xerri, challenging his three-match suspension for an incident that resulted in Melbourne midfielder Tom Sparrow being concussed.
While the Roos did not specify what their case would be, the most obvious argument would be that the grading should be accidental conduct, not careless.
The incident sparked a furious reaction from Melbourne on Sunday and Demons hard-nut Jack Viney made no apologies for "flying the flag" after Xerri knocked out Sparrow, who was stretchered off the MCG.
"To see a teammate go down like that is quite scary and hopefully Tom's OK," Viney told AAP.
"It didn't look great out there from Tom's perspective. Fingers crossed Tom will be on the mend in not too long."
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